q$-Deformed Chern Class, Chern-Simons and Cocycle Hierarchy
arXiv:hep-th/9403153 · doi:10.1088/0305-4470/28/3/011
Abstract
In this paper, from the -gauge covariant condition we define the -deformed Killing form and the second -deformed Chern class for the quantum group . Developing Zumino's method we introduce a -deformed homotopy operator to compute the -deformed Chern-Simons and the -deformed cocycle hierarchy. Some recursive relations related to the generalized -deformed Killing forms are derived to prove the cocycle hierarchy formulas directly. At last, we construct the -gauge covariant Lagrangian and derive the -deformed Yang-Mills equation. We find that the components of the singlet and the adjoint representation are separated in the -deformed Chern class, -deformed cocycle hierarchy and the -deformed Lagrangian, although they are mixed in the commutative relations of BRST algebra.